This application discloses an invention which is related, generally and in various embodiments, to a system and method for controlling a permanent magnet motor.
In many applications, a motor drive draws a three-phase fixed frequency alternating current from a power source and applies a three-phase variable frequency AC voltage to a portion of the motor referred to as the “stator”. The motor draws a three-phase variable frequency alternating current which causes a portion of the motor referred to as the “rotor” to rotate, and the rotation of the portion of the motor produces a torque which is utilized to deliver some type of mechanical energy or work. A controller is commonly utilized with the motor drive to control the torque and speed of the motor.
In general, one goal of motor control is to provide shaft torque as required to accelerate the shaft or sustain a prescribed rotational speed. For some time, it has been realized that transform methods are very helpful in this task since they allow viewing the stator currents as components relative to the rotating rotor frame of reference where the field interactions with the permanent magnet take place and steady torque is generated. The stator phase currents are commonly transformed to the rotor frame to obtain direct and quadrature axes components (i.e., d- and q-axes components). The two components of stator current physically represent two spatially orthogonal windings rotating synchronously with the rotor and producing the same fundamental magnetic field as that of the stationary phase windings themselves.
The d-axis component of the stator phase current produces flux that adds to the main rotating field established by the rotor permanent magnet. This component of current produces no torque on the rotor at all since it is directly aligned with the flux from the permanent magnet. It does, however, enhance or reduce the main flux that links the stator coils and induces a voltage.
The q-axis component of the stator phase current interacts directly with the rotor field to produce electromagnetic torque since it is spatially located in quadrature with the main permanent rotor flux. That is, the q-axis current peaks at the same spatial location as the rotor magnetic field peaks so that a Lorentz force exists and this creates electromagnetic torque on the rotor shaft. It is this component of current that the transform methods control in order to control rotor shaft torque and speed. Thus, the transform provides a method of decomposing the stator current into independent flux and torque producing components for the electromechanical control of the synchronous motor.
Three of the more commonly utilized control methods are (1) the maximum torque per ampere control method, (2) the maximum torque per volt control method, and (3) the constant volts per hertz control method, each of which are described in more detail hereinbelow.
Regarding the maximum torque per ampere control method, this method controls motor speed and torque by maintaining the d-axis component of motor current at zero while controlling the q-axis current to a value sufficient to establish the desired shaft torque. This method provides the maximum torque per ampere since all of the applied stator current is used to create torque and no current adding to or subtracting from the main rotor flux is generated. That is, the flux from the torque producing q-axis current produces a magnetic field that is spatially orthogonal to the main rotor flux. The main objective of the maximum torque per ampere control method is to command the required amount of q-axis current that is needed to produce torque while holding the d-axis current at zero. This is analogous to driving a dc motor where slip rings are used to spatially locate the armature current where the applied magnetic field peaks. All of the applied current produces torque in this type of motor. In theory, the amount of torque can be increased indefinitely by proportionally increasing the amount of quadrature axis current. The other component of current is kept fixed at zero so there is no effect on the applied d-axis field level.
The expression for electromagnetic torque from the fundamental interaction between the stator transformed current and the permanent magnet field for a three-phase motor may be expressed by the following equation:
                    T        =                              3            2                    ⁢                                    p              2                        ⁡                          [                                                                    λ                                          p                      ⁢                                                                                          ⁢                      m                                                        ⁢                                      i                    q                                                  +                                                      (                                                                  L                        d                                            -                                              L                        q                                                              )                                    ⁢                                      i                    q                                    ⁢                                      i                    d                                                              ]                                                          (        1        )            where T is the motor electromagnetic torque, p is number of motor poles, λpm is the stator flux linkage from the permanent magnet, iq is the amount of q-axis current, id is the amount of d-axis current, Ld is the motor stator d-axis inductance and Lq is the motor stator q-axis inductance. It should be noted that there are two components contributing to the torque in equation (1). The first component represents the interaction of the permanent magnet field (λpm) and the stator q-axis current (iq). This is the primary torque component obtained from the stator current located in the region of the main rotor flux. This component represents the fundamental electromagnetic torque generation associated with the synchronous motor. The second component is a reluctance torque arising from the difference in magnetic permeance (Ld−Lq) in the q- and d-axes flux paths. This component can be ignored for the case of the “maximum torque per amp” control since the d-axis current is driven to zero. This results in a torque in equation (1) that is exactly proportional to the q-axis current for the “maximum torque per amp” control method. It should be noted that although the d-axis current is zero for the “maximum torque per amp” control method, the d-axis flux is not zero because of the main rotor flux set up by the permanent magnet. The main rotor flux from the permanent magnet produces a flux linkage in the d-axis stator coil and is denoted by λpm.
Another variable of fundamental importance in motor control is the motor terminal voltage required to drive the q-axis current and establish the electromagnetic torque. The motor voltage can be viewed in terms of the rotor reference frame d- and q-axes quantities using the dq coupled equivalent circuit model of the motor taken from equation (1) and shown in FIG. 1. The motor voltage equations are obtained from the circuits in FIG. 1 and are given in the rotor frame of reference by the following steady-state equations:vq=rsiq+ωrλpm+ωrLdid  (2)vd=rsid−ωrLqiq  (3)
The currents and voltages are driven to dc quantities in the rotor frame of reference such that a steady torque is obtained. Consequently, since the steady-state behavior of the voltage equations is the primary concern, any voltage drops associated with the inductances in FIG. 1 can be ignored. The q-axis voltage equation contains a resistive voltage drop component that is proportional to the q-axis current. The product of the speed (ωr) and the permanent magnet flux linkage (λpm) represent the back emf in the motor q-axis circuit. There exists another voltage term proportional to speed and the current of the d-axis circuit. This cross-coupling speed voltage from the d circuit is a consequence of writing the voltage equations in the transformed variables. Likewise, a speed voltage component exists in the d-axis voltage equation where the voltage component is proportional to the speed times the q-axis current.
The general relationship between d-axis flux linkage and current is given by the following equation:λd=λpm+Ldid  (4)In the case of the q-axis, there is no flux linked from a rotor source. The permanent magnet only excites the d-axis flux so that the q-axis flux linkage is simply the product of the q-axis current and inductance as given in following equation:λq=Lqiq  (5)
In the case of “maximum torque per amp” control with light loading, the q-axis current and flux linkage is small (relative to the permanent magnet flux linkage) so it may be neglected. The resulting terminal voltage is dominated by the back emf induced in the q-axis circuit (i.e., flux linkage is primarily down the d-axis). This is desirable since the only component of current is in the q-axis in the “maximum torque per amp” control because id=0. The terminal current is precisely aligned and the terminal voltage is approximately aligned with the q-axis so that they both peak at nearly the same time. This implies the motor power factor is nearly unity for very light loading with the “maximum torque per amp” control.
As the shaft loading of the motor increases, the current, iq, and the corresponding flux linkage, λq (=Lq iq), increases as shown in FIG. 2. This flux linkage component is in quadrature with d-axis flux linkage (λpm) and the resultant flux linkage (λ) begins to increase. Additionally, a negative d-axis component of the speed voltage arises from the q-axis flux linkage so that the net terminal voltage contains both positive q- and negative d-axis components. The power factor angle at the motor terminals begins to increase as the shaft loading increases (i.e., voltage angle leads current angle). Eventually the shaft loading is great enough so the q-axis flux and corresponding negative d-axis speed voltage will become larger than the motor back emf from the permanent magnet itself. At this point the motor operates at a high flux level and a low power factor.
With the maximum torque per amp control method, the stator flux linkage is increased by approximately 40 percent at the point when the q-axis flux linkage is large enough to match the back emf. This increased flux level can result in magnetic saturation throughout the motor which makes the motor much less effective at high motor loading. This is in addition to operation at reduced power factor. It is clear that flux regulation at high motor loading can provide benefits to motor performance.
Regarding the maximum torque per volt control method, the method provides better regulation of the flux level at high motor loading than the maximum torque per amp control method. Flux reduction can be achieved with the maximum torque per volt control method by applying armature demagnetizing current with the d-axis circuit. The objective is to reduce the stator flux linkage and voltage by directly opposing the flux from the permanent magnet. This will have very little impact on the electromagnetic torque since the torque is controlled primarily by the motor q-axis current. However, the net stator operating flux linkage level will be reduced by the demagnetizing d-axis current. The demagnetizing current will improve the power factor at high motor loading since the terminal voltage also possesses both positive q-axis and negative d-axis components so that it tends to better align with the applied current. Thus, it will be appreciated that this method utilizes a “field reduction” or “field weakening” technique to reduce the operating flux while improving the motor power factor.
The demagnetizing d-axis current is combined with the q-axis current needed to provide motor shaft torque. The method provides torque at a minimum operating flux and voltage level. This method does require knowledge of the motor d-axis current required to completely neutralize the d-axis flux from the permanent magnet. Equation 4 provides the value of d-axis current required to produce zero net d-axis flux. This is the negative of the permanent magnet flux linkage (λpm) divided by the d-axis inductance (Ld). The stator d-axis current is held fixed at this level regardless of the value of the q-axis current that is used to regulate torque.
The equivalent motor circuit shown in FIG. 1 becomes simplified using the “maximum torque per volt” control method. The two voltage sources in the q-axis circuit are sized to exactly cancel each other so they can be eliminated from the circuit. The resulting circuit contains no speed voltage term so that the q-axis current is simply proportional to the q-axis voltage in the steady state. This simplifies the control since the cross coupling flux from the d-axis circuit is eliminated from consideration. However the d-axis circuit still contains the speed voltage from the q-axis flux linkage. In view of the foregoing, it will be appreciated that the maximum torque per volt control method eliminates a component of flux linkage as opposed to the maximum torque per amp control that eliminates a component of current.
Regarding the constant volts per hertz control method, the objective of this method is to keep the stator terminal volts per hertz or flux linkage at a fixed value independent of the level of motor loading. This method necessitates evaluating the level of demagnetizing d-axis current so that the volt per hertz magnitude is held constant. The condition of constant volts per hertz can be obtained using the steady state voltage equations. The voltage magnitude is the resultant of the q- and d-components given by equations (2) and (3). This control will adjust the d-axis current level such that the resultant voltage normalized by synchronous speed will be kept constant.
This method has the advantage that the magnetic operating point of the motor stator is more or less kept constant. Often the resistive component of voltage is neglected so only the stator flux linkage is controlled. Specifically, the resultant of the flux linkage vector given by equations (4) and (5) is controlled so that the stator flux linkage is fixed. Other variations of this method exist whereby the magnetizing component of the flux linkage is controlled rather than the total stator flux linkage. This often provides more precise control of the motor air gap magnetic operating point throughout a range of loads.
The level of the d-axis current required to hold the stator flux linkage constant is given by the following equation:
                              I          d                =                              -                                                  ⁢                                          λ                pm                                            L                d                                              +                                                                      λ                                      p                    ⁢                                                                                  ⁢                    m                                    2                                                  L                  d                  2                                            -                                                                    L                    q                    2                                    ⁢                                      I                    q                    2                                                                    L                  d                  2                                                                                        (        6        )            This result indicates that the condition of constant stator flux linkage can be maintained throughout a limited range of q-axis current. If the q-axis flux (Lq Iq) exceeds the permanent magnet flux (λpm) then there is no possible way of demagnetizing the magnet so that the resultant flux magnitude is held constant. This is because the q-axis flux has become so large that the resultant vector will increase in magnitude even if complete cancellation of the flux in the d-axis exists. The flux linkage can be held constant until the point when the demagnetizing current reaches its limiting value and the net d-axis flux is driven to zero. An alternative control must be pursued if greater motor loading is desired. Often this control is simply just continuing to minimize the flux increase by retaining the d-axis flux component at zero.